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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 35904.bz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35904.bz1 | 35904bf2 | \([0, 1, 0, -70918849, 163838024351]\) | \(150476552140919246594353/42832838728685592576\) | \(11228371675692555980242944\) | \([2]\) | \(6230016\) | \(3.5134\) | |
35904.bz2 | 35904bf1 | \([0, 1, 0, -26354369, -50062566753]\) | \(7722211175253055152433/340131399900069888\) | \(89163405695403920719872\) | \([2]\) | \(3115008\) | \(3.1668\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 35904.bz have rank \(1\).
Complex multiplication
The elliptic curves in class 35904.bz do not have complex multiplication.Modular form 35904.2.a.bz
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.